Forestieri opened the scoring from the penalty spot in the 15th minute with his fifth goal of the season - his second in two games - and was also involved when the Owls doubled their lead through Tom Lees after 29 minutes.
It was the first time in nine Sky Bet Championship games that Wednesday had scored more than one goal and helped earn the visitors their first win at Molineux in seven attempts, having lost on their last five visits.
They were well worth their success, and the result will have given Lambert a clear idea of the huge task ahead as Wolves slid deeper into trouble.
Wolves crashed to a fourth home straight defeat - and saw their winless run extended to nine games during which time they have collected only three points from a possible 27.
The hosts wasted a golden chance to open the scoring when Conor Coady and Jon Dadi Bodvarsson combined in the 11th minute.
Iceland international Bodvarsson set up Coady on the edge of the area but the former Huddersfield midfielder dragged his shot wide of Keiren Westwood's far post.
It was to prove to be a costly miss as Forestieri punished them four minutes later by winning and converting the penalty.
Referee Jeremy Simpson had no hesitation in pointing to the spot when Forestieri was brought down by full-back Matt Doherty. Forestieri then calmly sent Wolves goalkeeper Andy Lonergan the wrong way from 12 yards.
Wednesday should have doubled their advantage after 20 minutes but Barry Bannan's shot flew over the bar after good work from Ross Wallace.
But they did not have to wait much longer to make their growing dominance pay as they cut Wolves apart down the left wing.
Forestieri's cross flew across the face of the Wolves goal and was collected by Lucas Joao. He rolled the ball into the path of Lee, who had the simple task of steering his shot from 10 yards past the terribly exposed Lonergan.
Lambert sent on striker Nouha Dicko at half-time to try to inject some life into his side and they did have more purpose to their play in the second period.
Wednesday goalkeeper Westwood was finally forced into action when he was well placed to pluck out a header from Kortney Hause in the 63rd minute following a corner from Jack Price.
Wolves substitute Ivan Cavaleiro should then really have handed Lambert's side a lifeline after 77 minutes.
He was unmarked at the far post when Dave Edwards picked him out with a header, but he somehow managed to drag his shot right across the face of goal to perfectly sum up a dismal day for Lambert and Wolves.